7 3 special right triangles

Section 7-3Section 7-3spi.3.2.Gspi.3.2.G

Jim Smith JCHSJim Smith JCHS

Our First Special RightOur First Special Right Triangle Is A Triangle Is A 3,4,53,4,5

The Hypotenuse Must BeThe Hypotenuse Must Be

A Multiple Of 5 And A Multiple Of 5 And The Legs Must Be The Legs Must Be

Multiples Of 3 And 4Multiples Of 3 And 4

Use The Pythagorean Theorem To Find XUse The Pythagorean Theorem To Find X

33

33

xx xx55

559 + 9 = x²9 + 9 = x² 18 = x²18 = x² 18 = x18 = x

3 2 = x3 2 = x

25 + 25 = x²25 + 25 = x² 50 = x²50 = x² 50 = x50 = x

5 2 = x5 2 = x

13 213 2

7 27 2

Speed Trials 45, 45, 90Speed Trials 45, 45, 90

44

44

22

22 1313

1313

77

77

4 24 2

2 22 2

If 2 Sides Of A Triangle AreIf 2 Sides Of A Triangle AreCongruent, Then The Angles Opposite Congruent, Then The Angles Opposite

Them Are CongruentThem Are Congruent||

||

4545

4545

45, 45, 9045, 45, 90

Legs are equalLegs are equalLeg x 2 = hypLeg x 2 = hyp

||

||

4545

4545

45, 45, 9045, 45, 90

XXMult by 2 Mult by 2

X 2 X 2 XX

Going Backwards….DIVIDEGoing Backwards….DIVIDE

88

4545

8822

4 24 2

8822

22==

Div by 2Div by 2

8822

2222

==

4 24 2

4 24 2

30, 60, 90 Triangles30, 60, 90 TrianglesNo angles are equal soNo angles are equal sono sides are congruentno sides are congruent

3030

6060

LegLeg

LegLeg

HypHypShortShort

LongLong

30, 60, 90 Triangles30, 60, 90 Triangles

3030

6060

LegLeg

LegLeg

HypHypShortShort

LongLong

Mult by Mult by 22

30, 60, 9030, 60, 90

6060

303088

2 x 8 = 162 x 8 = 16

30, 60, 9030, 60, 90

6060

303055

2 x 5 = 102 x 5 = 10

30, 60, 9030, 60, 90

3030

6060

LegLeg

LegLeg

HypHypShortShort

LongLong

Mult by 3Mult by 3

30, 60, 9030, 60, 90

3030

6060 HypHyp1515

15 x 3 = 15 315 x 3 = 15 3

30, 60, 9030, 60, 90

3030

6060 HypHyp33

3 x 3 = 3 33 x 3 = 3 3

Going Backwards….DIVIDEGoing Backwards….DIVIDE

3030

6060SLSL

LLLL

HH1313

131322

For now, we’ll leave it as an improper fractionFor now, we’ll leave it as an improper fraction

3030

6060SLSL

LLLL

HH

5 35 3

5 35 333

= = 55

Going Backwards….DIVIDEGoing Backwards….DIVIDE

Going Backwards….DIVIDEGoing Backwards….DIVIDE

888833

3030

6060SLSL

LLLL

HH

3333

==88

3333

883333

30, 60, 90 30, 60, 90

3030 3030 3030999 39 3 22

9922

55

5 35 3 33

10 310 3 33 1212

66

6 36 3

What Do YouWhat Do YouKnow About Know About This Triangle?This Triangle?

|||||| 60606060

606030303030